The linear equation parallel to 8y=6x+5 is:
y = (3/4)*x - 4
How to find the equation of the parallel line?Remember that two linear equations are parallel if and only if both lines have the same slope and different y-intercept.
Here we want to find a line parallel to:
8y = 6x + 5
Rewriting this in slope-intercept form we get:
y = (6x + 5)/8
y = (3/4)*x + 5/8
Then a parallel line to this one will be:
y = (3/4)*x + b
To find the value of b, we use the fact that this line must pass through the point (-8, -10).
-10 = (3/4)*(-8) + b
-10 = -6 + b
-10 + 6 = b
-4 = b
Then the linear equation is:
y = (3/4)*x - 4
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a rectangular garden has a length of x and a y. the garden has its length reduced by 3 feet and its width extended by 2 feet. what is the area of the new garden?
The area of the new garden is found to be (x-3)(y+2) square units where x and y are the original dimensions.
What is the rectangle area formula?When calculating a rectangle's area, we multiply the length by the width of the rectangle.
What are examples of the area's practical applications?The area of the floors and walls must be measured before applying carpet or tiles on the floor, painting the walls, or installing cabinets in a space.
Given: A rectangular garden has x and y dimensions. The garden's width is increased by 2 feet while its length is decreased by 3 feet.
New length = x-3
New width = y+2
Area of new garden is given as:
=(length)(width)
= (x-3)(y+2)
Therefore, the area of the new garden is found to be (x-3)(y+2) square units where x and y are the original dimensions.
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On the interstate there is a ratio of 2 trucks to 4 cars to 3 SUVs, if there are a total of 1800 vehicles on the road, how many of each type of vehicle is on the road?
Answer:
Step-by-step explanation:
yes Saab do
If a, b, and c are positive prime numbers, in the equation a - b = c, either b or c must represent which number?
The value of prime numbers c in the equation is c = 2.
What is prime numbers?
Those greater than one are known as prime numbers. They simply have two variables, the number itself and factor 1.
We have given that a - b = c requires all of the integers to be positive prime numbers,
c can only have one outcome, which is 2.
[tex]e.g., 13 - 11 = 7 - 5 = 2.[/tex]
Hence in the given prime numbers c in the equation is c = 2.
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Triangles geometry . I really neeed it. Teacher don’t explain at all.
The value of x is 32.5°(degree) when isosceles triangle has a base angle of (4x-3)degrees and non base angle is 54 degrees.
How to calculate the value of x?We know that an isosceles triangles is composed of a vertex angle and two base angles. The base angles are congruent to each other. We also know that the sum of a triangle's angles is 180°(degrees).
According to given data,
⇒ 180 - {(4x-3)+54}= 0
⇒180 - 4x + 3 - 54 = 0
⇒130 = 4x
∴ x = 32.5°(degree).
That means that each base angle is 32.5°(degree).
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Complete both transformations below. Then enter the final coordinates of the figure. A (1.-2)
B (4,-1)
C (5.-3)
1) < -2.4 >
2) Dilate K = 3
Applying the transformation rule (x - 2.y + 4) and using the scale factor k = 3 for dilation gives
preimage translation image Dilation image
A (1.-2) A' (-1, 2) A'' (-3, 6)
B (4,-1) B' (2, 3) B'' (6, 9)
C (5.-3) C' (3, 1) C'' (9, 3)
What is transformation?Transformation is a term used in mathematics to refer to the movements made by objects.
Translation refers to a type of transformation that involve a linear movement.
Applying the transformation rule (x - 2.y + 4 ) gives
A (1.-2) = (1 - 2, -2 + 4) = (-1, 2)
B (4,-1) = (4 - 2, -1 + 4) = (2, 3)
C (5.-3) = (5 - 2, -3 + 4) = (3, 1)
preimage image
A (1.-2) A' (-1, 2)
B (4,-1) B' (2, 3)
C (5.-3) C' (3, 1)
Dilation involves making the image bigger or smaller. In this case K > 1 hence the image is bigger
Using the scale factor k = 3 for dilation rule (kx, ky) gives
A' (-1, 2) = (-1 * 3, 2 * 3) = (-3, 6)
B' (2, 3) = (2 * 3, 3 * 3) = (6, 9)
C' (3, 1) = (3 * 3, 1 * 3) = ( 9, 3)
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Can someone please help me
The proof that show show how ΔTRS ≅ ΔQRP by SAS congruence theorem is explained below.
What is the SAS Congruence Theorem?The SAS congruence theorem states that if two triangles have one pair of corresponding included angles that are congruent, and two pairs of corresponding sides that are also congruent, then both triangles are congruent to each other.
Using the SAS, the proof that shows both triangles are congruent is explained below.
Statements Reasons
1. SR ≅ PR 1. Given
2. SP bisects TQ 2. Given
3. TR ≅ QR 3. Definition of bisection
4. ∠TRS ≅ ∠QRP 4. Vertical ∠s theorem
5. ΔTRS ≅ ΔQRP 5. SAS congruence theorem
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Which answer choice shows 38.782 rounded to the nearest half? PLEASE HURRY IS DUE TODAY!!!!!!!!!!!
A. 38
B. 38.5
C. 39
D. 39.5
Bobbi wants to buy a bandana that costs 3.75$ But she has only 7.75$ in her budget what is her budget deficit
The budget deficit is how much less the budget is to buy a thing, thus Bobbi has the budget deficit as $3.75 - $0.75 = $3.00 thus option (B) is correct.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects.
In other meaning, subtraction is a mathematical operation such that two values are going to subtract and give a resultant value.
As per the given,
Cost of bandana = $3.75
Budget = $0.75
Budget deficit = $3.75 -$0.75
⇒ $3.00
Hence, "The budget deficit is how much less the budget is to buy a thing, thus Bobbi has the budget deficit as $3.75 - $0.75 = $3.00".
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The given question is incorrect, the correct question follows;
Bobbi wants to buy a bandanna that costs $3.75, but she has only $0.75 in her budget. What is her budget deficit?
A. $0.20
B.$ 3.00
C. $5.00
D.$4.50
The depth of the water on the shore of a beach varies as the tide moves in and out. The equation
D(t) = 0.75 cos (t) + 1.5 models the depth of the water, D(t), in feet and t as time in hours.
1. When will the tide be at its lowest for the first time when t > 0?
A) 3
B) 6
C) 9
D) 12
Answer:
C) 9 hours
Step-by-step explanation:
as per your picture the equation is
D(t) = 0.75×cos(pi/6 × t) + 1.5
the function cosine continuously "waves" from +1 to -1 and back.
the lowest value of this function for the first time after t>0 is when the cosine part reaches -1 the first time.
that is at 270° or 3pi/2.
so,
pi/6 × t = 3pi/2
1/6 × t = 3/2
t = 3×6/2 = 3×3 = 9
Commuting Distances (in miles)
The commuting distances in miles of 10 employees were used to make the box plot shown above. Which of the following is the median of the set of commuting distances? (please no long paragraphs or answers that aren't even there)
A. 30
B. 25
C. 28.5
D. 27.5
Answer:
The answer is gonna be B. Sorry if I’m late :((
Step-by-step explanation:
Answer: 25
Step-by-step explanation:
Find all possible values of x for which these two triangles are simliar.
Please help quickly!!!
The possible value of x which the two triangles are similar is x=60°.
What do you mean by triangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
Method:
Given that two angles of the triangle are specified, the triangles can be
similar for only one value of x.
According to the given data in the question,
The two triangles are similar when we have;
x + 10° = 2x - 50°
Which gives;
2x - x = 50° + 10° = 60°
x = 60°
Checking gives;
x + 10° = 2·x - 50° = 70°
Two angles of the first triangle are 70° and 60°
Then, the third angle of the first triangle is (180° - (70° + 60°)) = 50°
The three angles of the first triangle are therefore; 70°, 60° and 50°.
Two angles of the second triangle are 70° and 70°.
The third angle of the second triangle is (180° - (70° + 70°)) = 40°
The three angles of the second triangle are therefore; 70°, 70° and 40°
Therefore, the two triangles are similar by AAA similarity.
The two triangles are similar when, x = 60°
When x = 50°, we have;
x + 10° gives;
50° + 10° = 60°
∴ ∠(x + 10°) = 60°
The two angles of the first triangle are; 60° and 50°
The third angle on the second triangle is 180° - (60° + 50°) = 70°
On the second triangle, we have;
2·x - 50° gives;
2 × 50° - 50° = 50°
∴∠(2·x - 50°) = 50°
Therefore, the two angles of the second triangle are 70° and 50°
The third angle on the second triangle is 180° - (70° + 50°) = 60°
Therefore, the two triangles are not similar when x = 50°
Similarly, the two triangles are not similar when x + 10° = 50°
Hence, the possible value of x which the two triangles are similar is x = 60°.
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Sorrel has 54 beads, and 16 of them are red. Of the remaining beads, half are yellow and half are green. How many yellow beads does she have?
Sorrel has 19 yellow beads.
What is fraction?Fraction is a ratio of two integers.
Fraction is divided into two section by a dividing line and these sections are numerator and denominator.
Fractions are of different types: proper fraction, improper fraction and mixed numbers.
Total number of beads =54
if 16 are red, the remaining beads would be ( 54 - 16) = 38
Half of the remaining are yellow = 1/2 x 38
Then number of yellow beads = 19
And number of green beads = 38 - 19
= 19
In conclusion, the total number of yellow beads is 19
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Any nonzero integer divided by 0 equals 0.
Answer: False
Step-by-step explanation:
Can not divide a number by 0.
How do you graph this?
Reflection at point y = -6 will have coordinates as
preimage image
Q(0, -9) Q' (0, -6)
R(4, -9) R' (4, -6)
S(6, -8) S' (6, -5)
T(2, -8) T' (2, -5)
How to find the coordinatesThe transformation involve is reflection and this is a type of transformation that produces the mirror image of the preimage
The transformation rule to get the mirror image is (x, y) → (x, y + 3)
The coordinates are applied as follows
Q(0, -9) → (0, -9 + 3) → Q' (0, -6)
R(4, -9) → (4, -9 + 3) → R' (4, 6)
S(6, -8) → (6, -8 + 3) → S' (6, -5)
T(2, -8) → (2, -8 + 3) → T' (2, -5)
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The chart shows the distances, in miles, between three places.
a)Write down the distance
from Hereford to Chester.
b) Which town is 99 miles
from Kendal?
c)If Ellen drives from Kendal to
Hereford via Chester, how
many miles will she drive?
The spreadsheet that shows the distances between the cities, indicates that the distances between the cities are as follows;
a) From Hereford to Chester, the distance is 95 miles
b) Chester is the town that is 99 miles from Kendal
c) Ellen will have driven 201 miles if she drives from Kendal to Hereford through Chester
What is a spreadsheet?A spreadsheet application is used for the storage analysis, organization, and computation of data.
The interpretation of the distances in the chart which is in the form of a spreadsheet are;
The value in the cell corresponding to the distance from Kendal to Chester that is the cell which is on the same column as Kendal and on the same row as Chester is 99
Therefore, the distance from Kendal to Chester is 99 miles
The value in the cell that directly links Chester to Hereford that is the cell which is on the same column as Chester and on the same row as Hereford is 95
Therefore, the distance from Chester to Hereford is 95 miles
The value in the cell that connects Kendal to Hereford, that is the cell which is on the same column as Kendal and which is on the same row as Hereford is 201
Therefore the distance from Kendal to Hereford is 201 miles
a) The distance from Hereford to Chester is 95 miles
b) The town that is 99 miles from Kendal is Chester
c) The distance Ellen will have driven if she drives from Kendal to Hereford via Chester is 201 miles
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In the triangle below, with right angle G, suppose that m/F= (3x-14)° and mZH=(5x-16)°.
Find the degree measure of each angle in the triangle.
The degree measure of each angle in the triangle is
∠H = 59°
∠F = 39°
Angle sum property of triangle says that sum of all the triangle is always equal to 180°
∠G is given to us as 90°
So by applying the property we an say that
90 + (3x - 14) + (5x - 16) = 180
8x = 180 - 90 + 14 + 16
8x = 120
x = 15
∠H = 5x - 16
∠H = 5*15 - 16
∠H = 75 - 16
∠H = 59°
∠F = 3x - 14
∠F = 3*15 - 14
∠F = 45 - 14
∠F = 39°
Therefore ∠H = 59° and ∠F = 39°
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The magnitude, M, of an earthquake is represented by the equation M=23log(EE0) where E is the amount of energy released by the earthquake in joules and E0=104.4 is the assigned minimal measure released by an earthquake. To the nearest tenth, what would be the magnitude of an earthquake releasing 3.4⋅1014 joules of energy?
Magnitude of an earthquake releasing 3.4*10^14 joules of energy is M ≈ 6.754.
Given:
The magnitude, M, of an earthquake is represented by the equation M=2/3log(E/E0) where E is the amount of energy released by the earthquake in joules and E0=10^4.4 .
E = 3.4*10^14
M = 2/3*log(3.4*10^14 / 10^4.4)
= 2/3*log(13535643798.8)
= 2/3*10.1314
= 20.2628 / 3
M = 6.754
Therefore Magnitude of an earthquake releasing 3.4⋅1014 joules of energy is M ≈ 6.754.
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What are the solutions of the quadratic equation?
`2x^{2}+12x+18=0`
show work
The solutions for the quadratic equation:
2x^2 + 12x + 18 = 0
are:
x₋ = -5.55
x₊ = -0.4
How to solve the quadratic equation?
Remember that for a general quadratic equation:
a*x^2 +b*x + c = 0
The solutions are of the form:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
Here we have the quadratic:
2x^2 + 12x + 18 = 0
Then using the formula for the solutions we will get:
[tex]x = \frac{-12 \pm \sqrt{12^2 - 4*2*18} }{2*2} \\\\x = \frac{-12 \pm 10.2}{4}[/tex]
The two solutions of the quadratic equation are:
x₋ = (-12 - 10.2)/4 = -5.55
x₊ = (-12 + 10.2)/4 = -0.4
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What’s the inequality for the sum of a number w is more than -12? Please help it’s already missing
The sum of a number w is more than -12 becomes w > -12
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.
We have been given that the sum of a number w is more than -12.
Now the sum of a number = w
It is more than -12 means the inequality form as;
w > -12
Therefore, the overall expression becomes w > -12
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Alonso went to the store to buy some almonds. The price per pound of
the almonds is $7.25 per pound and he has a coupon for $3.50 off the
final amount. With the coupon, how much would Alonso have to pay to
buy 5 pounds of almonds? Also, write an expression for the cost to buy
p pounds of almonds, assuming at least one pound is purchased.
The required price of almond and expression are $32.75 and c= $7.25P - $3.5 respectively.
What is pound?Pound is unit used to measure weight of quantity. It is used by the English speaking peoples.It equal to the 16 ounces and 0.454 kilogram.
According to given information:Alonso has a coupon of $3.5, let us consider P pound of almond. And price per pound of almond is $7.25
So, equation for the cost,
Cost(c) = $7.25P - $3.5
Then, the price of 5 pound of almond = $7.25×5 - $3.5
⇒ $36.25 - $3.5 = $32.75
Thus, the price of 5 pounds of almond is $32.75.
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Make x the subject:
Q1) 9y-5x = 4
Answer:
x = 9/5 y - 4/5
Step-by-step explanation:
Make x the subject:
9y - 5x =4
Subtract 9y from each side
9y-9y - 5x =-9y+4
-5x = -9y +4
Divide each side by -5
-5x/-5 = -9y/-5 + 4/-5
x = 9/5 y - 4/5
Answer:
x = (9/5)y - (4/5)
Step-by-step explanation:
Given equation,
→ 9y - 5x = 4
Solving for the required value of x,
→ 9y - 5x = 4
→ -5x = -9y + 4
→ x = (-9y + 4)/-5
→ [ x = (9/5)y - (4/5) ]
Hence, value of x = (9/5)y - (4/5).
The cost
C
, in £, of a monthly phone contract is made up of the fixed line rental
L
, in £, and the price
P
, in £, of the calls made. Enter a formula for the cost and, enter the cost if the line rental is £20 and the price of calls made is £15.
The formula for the cost if the line rental is £20 and the price of calls made is £15 will be 20 + 15p.
How to calculate the cost?It should be noted that an expression is used to illustrate the relationship given between the variables.
In this case, the monthly phone contract is made up of the fixed line rental and the price represented by p.
The appropriate expression to illustrate this information will be:
= Fixed cost + Calls made
= 20 + 15(p)
= 20 + 15p
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Sascha owns stock in Lewis Corp, and she bought a $1,000 corporate bond. The bond pays 6.34% annual interest.
How much will Sascha receive in annual interest?
The amount that Sascha will receive in annual interest based on the information is $63.40.
How to calculate the interest?From the information, Sascha owns stock in Lewis Corp, and she bought a $1,000 corporate bond and the bond pays 6.34% annual interest.
In this case, it should be noted that the simple interest is calculated as:
Principal × Rate × Time
Principal = $1000
Time = 1 year
Rate = 6.34%
The interest will be:
= Principal × Rate × Time
= 1000 × 0.0634 × 1
= $63.40
The interest is $63.40.
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At a baseball game, a vender sold a combined total of sodas and hot dogs. the number of sodas sold was three times the number of hot dogs sold. find the number of sodas and the number of hot dogs sold.
The number of sodas sold is 168
The number of hot dogs sold is 56
Total of sodas and hot dogs=224
Let the number of sodas sold be s, and the number of hot dogs sold be s
So we have the following:
s=3h.................i
s+h=224..........ii
we solve the two equation to find the value of s and h,
From equation ii, s=224-h, replacing this in equation i, we have:
224-h=3h
224=4h
h=56
Now, s=3*56
=168
s=168
Number of sodas=168
Number of hot dog sold=56
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The complete question is given below;
A vender sold a combined total of 224 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
which multiplication table have 8 and 50
Answer:2
Step-by-step explanation:
2*4=8
2*25=50
Given the equation F(x)=3x-1 what is f(x+9)?
f(x+9) = 3x + 26.
Given equation:
f(x)=3x-1
f(x+9) = 3(x+9) - 1
= 3x + 3*9 - 1
= 3x + 27 - 1
= 3x + 26.
Therefore f(x+9) = 3x + 26.
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Given the speeds of each runner below, determine who runs the fastest.
i cant figure this out and its due soon pls help me
The person who runs fastest is Zach.
How to find the speed?Ron runs 9 feet per second: 9 ft/s
Zach runs 410 feet in 49 seconds:
410/49 ft/s
=8.36 ft/s
= 8.4 ft/s (Approximately)
Katie runs 1 mile in 412 seconds:
1 mile = 5280 ft
5280/412 ft/s
=12.8 ft/s
Noah runs 870 feet in 1 minute:
= 870/60 ft/s
= 14.5 ft/s
Hence,
Ron 9 feet per seconds
Zach 8.4 feet per seconds
Katie 12.8 feet per seconds
Noah 14.5 feet per seconds
So, Zach is the fastest.
Therefore the fastest is Zach.
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people enter a gambling casino at a rate of 1 every 2 minutes. (a) what is the probability that no one enters between 12:00 and 12:05? (b) what is the probability that at least 4 people enter the casino during that time?
The probability that no one enters between 12:00 and 12:05 is 0.082.
The probability that at least 4 people enter the casino during that time is 0.242
Given that people enter the casino at the rate of 1 every 2 minutes. A random variable X is defined as the number of people entering the casino between the time period of 12:00 and 12:05. Since we are given in the question that people enter the casino at the rate of 1 every minute, hence in the given time period they enter at the rate of 2.5.
P(X=0) = [tex]e^{-2.5}[/tex] = 0.082
Hence the probability that no one enters between 12:00 and 12:05 is 0.082.
The required probability is simply
P(X≥4) = 1 - P(X=0) - P(X=1) - P(X=2) - P(X=3)
= 1 - [tex]e^{-2.5}[/tex] - 2.5[tex]e^{-2.5}[/tex] - (((2.5)² / 2)[tex]e^{-2.5}[/tex] ) - (((2.5³)/3!)[tex]e^{-2.5}[/tex])
= 0.242
Hence, the probability that at least 4 people enter the casino during that time is 0.242
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A triangle has sides with lengths of 8 miles, 12 miles, and 17 miles. Is it a right triangle?
What is the image of ( 0 , − 8 ) (0,−8) after a reflection over the line y = x y=x?
Answer:
(- 8, 0 )
Step-by-step explanation:
under a reflection in the line y = x
a point (x, y ) → (y, x ) , then
(0, - 8 ) → (- 8, 0 )